A model-selection-based unit-root detection by using the Bayesian information criterion is proposed. First, six alternative model classes are obtained considering the presence or absence of a unit root and considering three kinds of deterministic terms: no constant, constant, constant and trend. Second, given the selected model class, the best model is selected from the alternative models with different lags. Third, the best of the entire model set comprising the six models obtained in the preceding step is selected. Finally, whether an observed time series contains a unit root is determined on the basis of the selected model. Simulation results suggest that the proposed method is at least comparable to and often better than the sequential testing method provided by Dolado et al. (1990). Empirical results obtained by the proposed method are more convincing than those obtained by the sequential testing method and suggest that the hysteresis hypothesis can be applied to monthly time series of the unemployment rates for all the six countries under consideration.